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A307805 a(n) = first position of prime(n) in A023503. 1

%I

%S 2,4,5,10,9,16,27,43,15,17,64,35,23,40,61,28,127,73,57,104,62,66,39,

%T 41,77,111,114,117,182,49,97,56,143,102,196,155,248,119,346,69,72,181,

%U 76,137,497,139,318,388,721,401,91,92,229,96,243,249,325,258,186,103

%N a(n) = first position of prime(n) in A023503.

%C A023503(n) = A006530(A006093(n)).

%C Apparent permutation of A071349(n) apart from A071349(1) = 1.

%C Let i = a(n). Sorting prime(n) in order of increasing i yields A112037 = {2, 3, 5, 11, 7, 23, 13, 29, 41, ...}. The product of the first j terms of A112037 = A071350(j).

%H Rémy Sigrist, <a href="/A307805/b307805.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 2 since prime(1) = gpf(prime(2) - 1), i.e., 2 = gpf(2).

%e a(2) = 4 since prime(2) = gpf(prime(4) - 1), i.e., 3 = gpf(6).

%e a(3) = 5 since prime(3) = gpf(prime(5) - 1), i.e., 5 = gpf(10).

%e a(4) = 10 since prime(4) = gpf(prime(10) - 1), i.e., 7 = gpf(28).

%t With[{s = Array[FactorInteger[Prime@ # - 1][[-1, 1]] &, 1000]}, Reap[Do[If[FreeQ[s, #], Break[], Sow@ FirstPosition[s, #][[1]]] &@ Prime@ i, {i, Length@ s}]][[-1, -1]]]

%o (PARI) { a = vector(60); pr = primes(#a); u = 1; n = 1;

%o forprime (p=3, oo, n++; f=factor(p-1); g=setsearch(pr, f[#f~,1]);

%o if (g && !a[g], a[g]=n; while (a[u], print1 (a[u]", "); u++; if (u>#a, break (2))))) } \\ _Rémy Sigrist_, May 28 2019

%Y Cf. A006093, A006530, A023503, A071349, A112037.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Apr 29 2019

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Last modified July 5 06:34 EDT 2020. Contains 335459 sequences. (Running on oeis4.)